Equation 1)  5x - 9y = -43
Equation 2)  3x + 8y = 68
Multiply equation 1 by 3, and equation 2 by 5.
1)  3(5x - 9y = -43)
2)  5 (3x + 8y = 68)
Simplify.
1)  15x - 27y = -129
2)  15x + 40y =  340
Subtract equations from each other.
-67y = -469
Divide both sides by -67
y = 7
Plug in (7) for y in equation 1
5x - 9y = -43
5x - 9(7) = -43
Simplify.
5x - 63 = -43
Add 63 to both sides.
5x = 20
Divide both sides by 5.
x = 4
(4, 7)
~Hope I helped!~